One (rough) way to look at it is using formulas is probably ~60% accurate, a proper heart-rate monitor is about 80% accurate, and a power meter is about 90% accurate. That's a complete SWAG on my part but the ratio between the three is probably along those lines.

I've seen over time that rides up to medium-high intensity seem to be less kJ worked than the HRM calculates for the same effort, whereas intense rides are always higher. But either ways the difference is 10% or less.

One thing I've learned over time is that if you are really trying to drop weight it's best to do it in a low intensity part of your rising season. For me, anyway, once I'm consistently over 5 hours of riding a week, my appetite makes it neigh impossible to keep a calorie deficit going.